The brainstem is the major route through which the brain sends information to and from the spinal cord and peripheral nerves. The brainstem controls, among other things, respiration and the regulation of heart rhythms.
The cerebrum is the largest part of the human brain. It is associated with higher order functioning, such as thinking, perceiving, planning, and understanding language, as well as controlling voluntary behavior.
The cerebellum is a large structure located at the roof of the hindbrain that helps coordinate movement by making connections to the pons, medulla, spinal cord, and thalamus. It also may be involved in aspects of motor learning.